Stabilizing surface for flight deck or other uses

ABSTRACT

A mechanism for maintaining a surface such as a landing pad in a desired orientation with respect to a supporting surface includes a pair of columns that rotate with respect to each other. The angle at which the columns engage, or the angle at which the columns engage the surface and the supporting surface, are offset with respect to a line perpendicular to the longitudinal axis of the cylinders. By selectively rotating the columns with respect to each other and with respect to the supporting surface, the tilt and orientation of the surface are adjusted.

CROSS-REFERENCES TO RELATED APPLICATIONS

The present application is a continuation-in-part of U.S. patentapplication Ser. No. 11/039,548, filed Jan. 19, 2005 now U.S. Pat. No.7,040,247, which claims the benefit of U.S. Provisional Application Ser.No. 60/539,922, filed Jan. 28, 2004, which is herein incorporated byreference.

FIELD OF THE INVENTION

The present invention relates to a mechanism for moving a surface in adesired orientation, and in particular to a mechanism for maintaining asurface such as a landing pad in a level orientation.

BACKGROUND OF THE INVENTION

In many environments, it is useful to have a surface which is levelregardless of the orientation of the structure supporting the surface.For example, helicopters or other vehicles including fixed-wing UnmannedAerial Vehicles (UAVs) and rotary-wing Vertical Take-off Unmanned AerialVehicles (VTUAVs) often need a level surface from which they can takeoff and land in a wide range of sea conditions. Providing such a surfaceis not a problem on land-based facilities or other structures that aresecured to a solid surface such as oil drilling platforms that areanchored to a sea bed, etc. However, providing such a surface can bedifficult when the object on which the aircraft is to land can move. Forexample, helicopters attempting to take off and land on ships arecurrently limited to a relatively narrow range of sea conditions inorder to avoid injuring the aircraft and/or crew.

Given these problems, there is a need for a mechanism that can beoperated to maintain a surface in a desired orientation regardless ofthe fact that the support for such a surface is not level and/or ismoving.

SUMMARY OF THE INVENTION

To address the problems discussed above, the present invention is amechanism for maintaining a surface in a desired orientation regardlessof the orientation and/or movement of the supporting structure. Forexample, the mechanism may be located on a ship to maintain a landingpad in a substantially level orientation regardless of the movement ofthe ship in the water. In other embodiments, the mechanism may be usedin a movable vehicle to maintain a stretcher or other equipment in alevel orientation.

In one embodiment of the invention, the mechanism comprises at least twocolumns such as an upper and lower cylinder having a pair of engagingsurfaces about which the cylinders rotate with respect to each other.The engaging surfaces are oriented at an angle with respect to a lineperpendicular to the longitudinal axis of the cylinders. When the upperand lower cylinder sections rotate with respect to each, the anglebetween the longitudinal axis of each cylinder varies. A surface to bemaintained in a desired orientation is secured to the upper cylinder andis coupled to a structure that supports the cylinders through a linkage.The tilt of the surface is selectively adjusted by rotating the upperand lower cylinders with respect to each other. The upper and lowercylinders may be rotated by electric motors or hydraulic, or pneumaticpistons or other mechanisms. The orientation of the surface is adjustedby rotating the upper and lower cylinders with respect to the supportstructure.

In another embodiment of the invention, the engaging surfaces of theupper and lower cylinders are oriented in a direction that isperpendicular to the longitudinal axis of the cylinders. The upper andlower cylinders engage the surface to be maintained in a desiredorientation and the supporting structure at an angle such that rotationof the upper cylinder with respect to the lower cylinder causes the tiltof the surface to change.

A position sensor, such as a gyroscope, measures the orientation of thesurface or the supporting structure. Signals from the position sensorare fed to a computer or other processor that calculates the desiredrelative position of the upper and lower cylinders in order to maintainthe surface in a desired orientation.

BRIEF DESCRIPTION OF THE DRAWINGS

The foregoing aspects and many of the attendant advantages of thisinvention will become more readily appreciated as the same become betterunderstood by reference to the following detailed description, whentaken in conjunction with the accompanying drawings, wherein:

FIG. 1 illustrates one environment where the mechanism of the presentinvention may be used;

FIGS. 2A and 2B are simplified illustrations of a mechanism formaintaining a surface in a desired orientation in accordance with oneembodiment of the present invention;

FIG. 3 is a cross-sectional view of one embodiment of a mechanism formaintaining a surface in a desired orientation in accordance with thepresent invention;

FIG. 4 illustrates another embodiment of a mechanism for maintaining asurface in a desired orientation in accordance with the presentinvention;

FIGS. 5A and 5B illustrate one embodiment of a bearing surface between afirst and a second cylinder;

FIG. 6 illustrates an embodiment of the invention having threecylinders;

FIG. 7 illustrates an embodiment of a computer system used in amechanism of the present invention;

FIG. 8 illustrates an embodiment of the invention having a pair ofcylinders with unequal diameters;

FIG. 9 illustrates one embodiment of a locking mechanism for inhibitingmovement of the cylinders;

FIGS. 10A–10C illustrate orientations of the mechanism for derivingformulas to change a position signal to desired relative positions ofthe cylinders;

FIG. 11 shows yet another embodiment of the invention that can be usedto move a mirror or other surface in a desired orientation;

FIG. 12 shows another embodiment of a linkage mechanism in accordancewith the present invention;

FIG. 13 illustrates yet another embodiment of a mechanism formaintaining a surface in a desired orientation in accordance with thepresent invention; and

FIG. 14 illustrates another embodiment of a mechanism for maintaining asurface in a desired orientation in accordance with the presentinvention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

As indicated above, the present invention is a mechanism for maintaininga surface in a desired orientation when supported by a moving ornon-level support structure. Although the following discussion describesthe invention for use in maintaining a surface such as a landing pad ina level orientation, it will be appreciated that the invention can beused in any environment where it is desirable to maintain a surface in adesired orientation despite the orientation or movement of thesupporting structure. For example, the present invention can be used tokeep beds or stretchers level inside an ambulance, helicopter or rescueplane, or can keep the entire patient cabin of the ambulance levelduring motion. Furthermore, the present invention can be used inhospital ships to stabilize the infirmary and surgery cabin.Alternatively, the present invention can be used in a medical laboratoryto stabilize a centrifuge or to keep other equipment from breaking.Also, the present invention can be used with offshore drilling to keepconstruction equipment on a level surface. Also, the present inventioncan be used to keep appliances and accessories level in pleasure craftas in sailboats, or in a vessel, such as keeping the stove in the galleylevel. Furthermore, it can be used to stabilize guns and artillerymounted on a ship or a moving vehicle. The present invention could beused as an earthquake reducer of a pedestal, a cupboard, room or a smallbuilding as for example in a museum or for stabilizing cameras mountedin an unstable environment. The present invention can also be used toimprove motion sickness by stabilizing a special cabin on a vehicle suchas a train or in a vessel.

The present invention can also be used to selectively orient a surfacesuch as a mirror to produce a light scanner, such as for bar codes. Thepresent invention can be used as a ride in an amusement park, exerciseor athletic equipment for balancing and for therapeutic messageequipment. The invention can be used by mounting a spot light forspecial attractions and events. Also it can be used in industrialautomation and machinery. The present invention could be used withfloating foundations for bridges over water if the GPS speed to keepelevation constant improves. Furthermore, these various applications ofthe invention and potentially others can be built of any small or largesize.

FIG. 1 illustrates one environment where the present invention may beused. In the example shown, a ship 10 has a landing pad 20 on its reardeck. The ship 10 may assume a variety of orientations due to wind,waves, load, or the like. The landing pad 20 is maintained in a levelorientation by the present invention so that a helicopter 30 or othervehicle can land on the landing pad 20 under a variety of weatherconditions or when the movement of the ship would cause a fixed landingpad to vary in orientation.

As will be explained in further detail below, position sensors on theship or a dedicated position sensor that measures the orientation of thelanding pad signals a computer system or programmed processor to adjustthe pitch and roll of the landing pad 20 so that it is continuallyoriented in a substantially level plane.

FIGS. 2A and 2B illustrate a simplified version of one embodiment of amechanism for maintaining a surface in a desired orientation accordingto the present invention. The mechanism 100 includes at least two, andpreferably a pair of columns comprising cylinders 102, 104 or othershapes that are rotatably engaged at an engaging surface 105 that cutsthrough the cylinders at an angle, ε, with respect to a line that isperpendicular to the longitudinal axis of the cylinders 102, 104. Alanding pad 20 is coupled to a top rim 106 of the upper cylinder 102 ina direction perpendicular to the longitudinal axis of the cylinder 102.A bottom rim 108 of the lower cylinder 104 is coupled to a structurethat can move such as a ship deck or hull. As shown in FIG. 2B, byrotating the upper cylinder 102 with respect to the lower cylinder 104about the angled engaging surface 105, the tilt of the landing pad 20 isvaried if the position of the bottom cylinder 104 is fixed.Alternatively, the orientation of the lower cylinder 104 is changed ifthe orientation of the landing pad 20 is fixed. In the embodiment shown,the present invention operates by sensing the orientation of thesupporting structure of the mechanism 100 or the orientation of thelanding pad 20 and selectively positioning the upper cylinder 102 withrespect to the lower cylinder 104 or vice versa and/or by rotating bothcylinders together such that the landing pad 20 remains relatively leveldespite changes in the orientation of the structure that supports thecylinders.

FIG. 3 is a cross-sectional view of one embodiment of a mechanism formaintaining the orientation of a surface such as a landing pad accordingto the present invention. As indicated above, the mechanism 100 includesan upper cylinder 102 that is rotatably coupled to a lower cylinder 104.The bottom of the lower cylinder 104 is supported on a surface 150 by aslew bearing 156 or other friction reducing mechanisms. In oneembodiment, the bottom surface of the lower cylinder 104 includes one ormore spur gears 154 that rotate the lower cylinder 104 within the slewbearing 156. A set of small slew bearings 152 support the spur gears 154on the surface 150. On the outer radius of the spur gear 154 are anumber of gear teeth (not shown) that engage gears 158 coupled to motors160. The motors 160 are supported by motor brackets 162 that are in turnsecured to the surface 150. The motors 160 cause the lower cylinder 104to rotate within the slew bearing 156 in order to adjust the position ofthe lower cylinder 104 with respect to the surface 150.

The upper cylinder 102 and lower cylinder 104 are rotatably coupled at apair of engaging surfaces 170, 172. Preferably, the engaging surface 172of the lower cylinder 104 has a lip or ledge 173 that supports theengaging surface 170 of the upper cylinder 102. A slew bearing 175supported by the lip 173 reduces friction between the engaging surfaces170, 172. Preferably, the slew bearing 175 is secured to the cylindersto accommodate the slightly oval shape of the engaging surfaces 170, 172in accordance with the angle at which they are cut through the cylinders102, 104. Alternately, other mechanisms such as ball bearings,Teflon-coated surfaces or other mechanisms could be used to reducefriction between the two cylinders and replacing slew bearings 175 andslew bearings 156 and 196.

As indicated above, the angle of the engaging surfaces 170, 172 isoffset with respect to a line perpendicular to the longitudinal axis ofthe cylinders 102 and 104. Therefore, by rotating the cylinders 102, 104with respect to each other, the angle between the longitudinal axes ofthe top and bottom cylinders is varied. A landing pad 180 or otherstructure is supported on the top rim of the upper cylinder 102 by anumber of beams 182 or other supports. Preferably, the landing pad 180is oriented in a direction perpendicular to the longitudinal axis of theupper cylinder 102.

Supported by the beams 182 are one or more motor brackets 190 that holdmotors 192. The motors 192 drive spur gears 194, which are mounted onsmall slew bearings similar to slew bearings 152 to engage a set ofinternal teeth of a slew bearing 196 that is positioned around the toprim of the upper cylinder 102. A portion of the slew bearing 196 aroundthe upper cylinder is mounted on the bottom surface of the beams 182 toconstrain the movement of the upper cylinder with respect to the beams182 in a generally circular path.

The landing pad 180 is held in a fixed relation with respect to thesurface 150 such that the frame of reference between the two remainsfixed. A linkage 200 having a pair of link arms 202 and 204 couple thelanding pad 180 to the surface 150. The link arm 202 is coupled at oneend to the beams 182 with a hinge 206 and at the other end is coupled tothe link arm 204 with a hinge 208. One end of the link arm 204 iscoupled to the link arm 202 with the hinge 208 and at the other end iscoupled to the surface 150 with a hinge 210. Each of the hingespreferably allow movement in a plane but not rotation in a plane. In oneembodiment, each of the hinges 206, 208, 210 is a universal joint thatmaintains the frame of reference of the landing pad 180 and the surface150. Also, the hinges 206, 208, 210 absorb the load caused by deflectionof the landing pad 180. Operation of the motors 160 cause the upper andlower cylinders 102, 104 to rotate with respect to the surface 150.Similarly, operation of the motors 192 cause the upper cylinder 102 torotate with respect to the bottom cylinder 104 in order to change thetilt of the landing pad 180.

Although the motors 160, 192 and their associated gears are shown on theinterior of the two cylinders 102, 104, it will be appreciated that themotors or other mechanisms such as pneumatic or hydraulic pistons forrotating the cylinders could be located outside of the cylinders.However, it is generally preferable to locate the motors or other meanson the interior of the surfaces to save space and to aid in protectingthem from moisture or other harsh environments.

As indicated above, a position sensor such as a gyroscope 212 senses theposition of the landing pad 180. The sensor can be mounted on the top orbottom deck. The signals from the gyroscope 212 are fed to a computer orother processor (not shown) that determines the appropriate amount bywhich the upper cylinder 102 should be rotated with respect to the lowercylinder 104. Once the desired tilt of the landing pad 180 has beenobtained by appropriately adjusting the relative position of the uppercylinder 102 with respect to the lower cylinder 104, both cylinders 102,104 can be moved by the motors 160 and 192 with respect to the surface150 in order to orient the landing pad 180 in a desired direction.

In another embodiment, the position sensor 212 may be mounted to measurethe orientation of the surface 150 such as the pitch and roll of a ship,stretcher, airplane, etc. The signals from the position sensor 212 arethen used by a computer to adjust the relative positions of thecylinders to maintain the landing pad 180 in a substantially levelorientation.

In the embodiment of the invention shown in FIG. 3, the engagingsurfaces 170, 172 of the upper and lower cylinders 102, 104 are cut atan angle of 7.5° with respect to a line perpendicular to thelongitudinal axis of the cylinders. Therefore, the maximum tilt that canbe obtained between the two cylinders is 15°. However, it will beappreciated that other angles could be used to provide more or less tiltif desired.

FIG. 3 also shows a position sensor 210 such as a bar code reader thatcan be used on the upper and lower cylinder to determine the position ofthe cylinders with respect to the supporting surface 150 or the landingpad 180. Signals from the position sensors can be fed to a computersystem to adjust the position of the cylinders if necessary.

FIG. 4 illustrates another embodiment of a mechanism for maintaining asurface in a desired orientation in accordance with the presentinvention. In this embodiment, a surface such as a landing pad 300 issupported by a number of beams 302 or other support structures thatmaintain the surface relatively flat. Supporting the beams 302 above asurface 320 are a pair of cylinders 306, 308. An upper cylinder 306 anda lower cylinder 308 have a pair of engaging surfaces 310, 312 aboutwhich the two cylinders rotate with respect to each other.

In this embodiment, the engaging surfaces 310, 312 are cut through thecylinders at an angle that is perpendicular to the longitudinal axis ofthe cylinders. The lower cylinder 308 has a bottom surface or rim 314that engages the surface 320 via a slew bearing 342 and the uppercylinder 306 includes a top surface or rim 322 that engages the bottomsurface of the beams 302 via a slew bearing 370. In this embodiment, thebottom surface or rim 314 of the lower cylinder 308 and the top surfaceor rim 322 of the upper cylinder 306 are angled with respect to a lineperpendicular to the longitudinal axis of the cylinders.

As with the previously described embodiment, the lower cylinder 308 hasa spur coupled to the lower cylinder 308 to accommodate the slight ovalshape of the bottom rim of the lower cylinder that engages the surface320. An outer diameter of the spur gear 340 has gear teeth (not shown)that engage gears 344 of a pair of motors 348. The motors 348 aresecured by a motor bracket 350 to the surface 320. Operation of themotors 348 cause the spur gear to rotate and to move the lower cylinder308 and the upper cylinder 306 in the slew bearing 342 with respect tothe surface 320.

On the top surface, the beams 302 support one or more motors 360 withmotor brackets 362. Gears 364 of the motors 360 engage a spur gear 372that in turn meshes with a geared slew bearing 370 that surrounds thetop rim of the upper cylinder 306. The spur gear 372 is supported by aset of small slew bearings similar to slew bearings 338. The slewbearing 370 constrains the movement of the upper cylinder to rotationwith respect to the beams 302. As with the slew bearing 342, the slewbearing 370 should be coupled to the upper cylinder to allow for theslightly oval shape of the top rim 322 of the upper cylinder 306.

Coupling the landing pad 300 to the fixed surface 320 is a linkagemechanism 380 including a pair of arms 382, 384. The arm 382 is coupledto the beams 302 with a movable hinge joint 386 and to the arm 384 witha movable hinge joint 388. The arm 384 is coupled at one end to the arm382 at the hinge joint 388 and at the other end to the surface 320 witha hinge joint 390. In one embodiment, the hinge joints 386, 388 and 390allow movement in a single plane but not rotation of the plane. In oneembodiment, the hinge joints 386, 388 and 390 are universal joints. Thehinge joints 386, 388 and 390 also absorb the load caused by deflectionof the landing pad 300.

Although the embodiments shown above use three universal joints tocouple the top surface to the supporting surface, it will be appreciatedthat the embodiment shown in FIG. 3 may be constructed with a singleuniversal joint and the embodiment shown in FIG. 4 could be constructedwith two universal joints, depending on the expected load the system isdesigned to carry. Similarly, although the disclosed embodiments usespur gears to couple the motors to the gears of the slew bearings, itwill be appreciated that other gear arrangements could be used to drivethe cylinders.

A position sensor 400, such as a gyroscope, provides signals regardingthe orientation of the landing pad 300. The sensor can be mounted on thetop or bottom deck. Signals from the sensor 400 are provided to acomputer or programmed processor (not shown) that calculates how theupper and lower cylinders 306, 308 should be rotated with respect toeach other and with respect to the surface 320 in order to adjust therelative position or tilt of the landing pad 300. As described above,the cylinders 306, 308 are rotated relative to each other in order tomaintain the landing pad 300 in a relatively level orientation. Relativemovement of the upper cylinder 306 with respect to the lower cylinder308 causes the tilt of the landing pad 300 to change. The direction oftilt can be changed by rotating the lower cylinder 308 and the uppercylinder 306 together with respect to the surface 320 using the motors348 and 360.

Although the described embodiments have the position sensors 212, 400 onthe landing pad or coupled thereto, will be appreciated that the sensorscould also be placed so that they determine the orientation of thesurface supporting the cylinders. In this configuration, signals fromthe sensors are supplied to a computer or programmed processor todetermine how the two cylinders should be rotated with respect to eachother in order to adjust the tilt and orientation of the landing padsuch that the landing pad is maintained substantially level.

The level adjusting mechanism shown in FIG. 4 may also include aposition sensor such as an optical bar code reader 410 to determine theposition of the cylinders with respect to the landing pad and thesupporting surface. Signals from the position sensors 210, 410 are fedto the computer system in order to aid in confirming that the cylindershave been correctly aligned to keep the landing pad level.

FIGS. 5A and 5B illustrate one mechanism for reducing friction betweenthe two engaging surfaces of the cylinders. The engaging surface of thelower cylinder wall 450 has a rim with a widened top surface 452 onwhich the upper cylinder rests. A number of wheels 462 are integrated orsecured to the engaging surface of the upper cylinder and ride on thewidened surface 452. If the engaging surfaces of cylinders are orientedat an angle with respect to the longitudinal axis of the cylinders, thenthe widened rim should have a width which allows for the slightly ovalshape of the two engaging surfaces while still allowing them to rotatewith respect to each other. A cover 470 forms a shallow U-shaped channelover the engaging surfaces to prevent the upper cylinder from slippingoff the lower cylinder. The cover 470 is secured to the outer diameterof the upper or lower cylinder. A wheel 472 or other bearing is orientedradially outward from the upper cylinder to reduce friction between thecylinders. A second wheel 474 rides within the U-shaped channel andhelps maintain the alignment of the cylinders. The cover 470 thereforereduces friction between the cylinders and helps maintain theiralignment as the cylinders rotate with respect to each other.

As indicated above, the present invention operates by adjusting therelative orientation of the cylinders in order to maintain the surfacesecured to the upper cylinder in a desired orientation. To determine thedesired position of the upper cylinder with respect to the lowercylinder, signals from the position sensor are fed to a computer orprogrammed processor that converts the signals into a desired positionof the cylinders. The following describes one possible technique forperforming the transformation of sensor signals to desired cylinderpositions. However, it is understood that other mathematical transformscould also be used.

For the embodiment shown in FIG. 3, the mechanism is a cylinder cut inthe center with an angle ε and it rotates at the bottom, top, andinclined surface. See FIG. 10A.

The mathematical transformation can be found as follows: from geometrystarting with the plane on the middle surface the plane equation is:−y tan ε+z=0  (1)

With the axis at the middle surface, rotation in the xy plane in thex-axis by an angle β yields the following plane equation:−x sin β−y cos β+z cot ε=0  (2)

Thus, β is the angle describing the rotation of both cylinders againsteach other to achieve the tilt. Now rotate in the yz-plane the y-axis byan angle ε so that the xy-plane can coincide with the vertical. Thus,the plane equation becomes:−x sin β+y(1−cos β)cos ε+z(sin ε cos ε+cos ε cot ε)=0  (3)

Thus at β=0 z=0 and β=±πz=−y tan2ε the maximum slope with the y axisrotated by ±π.

Now, rotate in the xy plane the x-axis by an angle α to yield the planeequation:x{−cos α sin β+(1−cos β)cos ε sin α}+y{sin αsin β+(1−cos β)cos ε cosα}+z(sin ε cos β+cos ε cot ε)=0  (4)

Thus, α is the angle describing the location of the tilt due to rotatingboth cylinders together.

The plane equation with respect to the tilt values from the positionsensor with the same frame of reference is:x tan z ₁ +y tan z ₂ +z=0  (5)

Where z₁ and z₂ are the tilt in the x and y direction with respect tothe bottom surface where the sensor is at the bottom surface.

Matching Eq. 5 with Eq. 4 yields

$\begin{matrix}{{{\tan\; z_{1}} = \frac{{{- \cos}\;\alpha\;\sin\;\beta} + {( {1 - {\cos\;\beta}} )\cos\;{ɛsin}\;\alpha}}{{\sin\; ɛ\;\cos\;\beta} + {\cot\; ɛ\;\cos\; ɛ}}}{and}} & (6) \\{{\tan\; z_{2}} = \frac{{{- \sin}\;\alpha\;\sin\;\beta} + {( {1 - {\cos\;\beta}} )\cos\;{ɛcos}\;\alpha}}{{\sin\; ɛ\;\cos\;\beta} + {\cot\; ɛ\;\cos\; ɛ}}} & (7)\end{matrix}$

From Eq. 6 and Eq. 7 they can be rewritten as:

$\begin{matrix}{{\tan\; z_{1}} = {{{- a_{1}}\cos\;\alpha} + {a_{2}\sin\;\alpha}}} & (8) \\{{{\tan\; z_{2}} = {{a_{1}\sin\;\alpha} + {a_{2}\cos\;\alpha}}}{{Where}\text{:}}} & (9) \\{a_{1} = \frac{\sin\;\beta}{{\sin\; ɛ\;\cos\;\beta} + {\cot\; ɛ\;\cos\; ɛ}}} & (10) \\{a_{2} = \frac{( {1 - {\cos\;\beta}} )\;\cos\; ɛ}{{\sin\; ɛ\;\cos\;\beta} + {\cot\; ɛ\;\cos\; ɛ}}} & (11)\end{matrix}$

From squaring Eq. 8 and Eq. 9 α is eliminated as follows:

$\begin{matrix}{{{{\tan^{2}z_{1}} + {\tan^{2}z_{2}}} = {a_{1}^{2} + a_{2}^{2}}}{Or}{{{\tan^{2}z_{1}} + {\tan^{2}z_{2}}} = \frac{{\sin^{2}\beta} + {( {1 - {\cos\;\beta}} )^{2}\cos^{2}ɛ}}{( {{\sin\; ɛ\;\cos\;\beta} + {\cot\; ɛ\;\cos\; ɛ}} )^{2}}}} & (12)\end{matrix}$

Solving for α from Eq. 8 and 9 yields:

$\begin{matrix}{{\sin\;\alpha} = \frac{{a_{2}\tan\; z_{1}} + {a_{1}\tan\; z_{2}}}{{\tan^{2}z_{1}} + {\tan^{2}z_{2}}}} & (13) \\{{\cos\;\alpha} = \frac{{{- a_{1}}\tan\; z_{1}} + {a_{2}\tan\; z_{2}}}{{\tan^{2}z_{1}} + {\tan^{2}z_{2}}}} & (14)\end{matrix}$

Substituting sin² β=1−cos² β in Eq. 12 and solve for β from thequadratic equation yields:

$\begin{matrix}{\beta = {{\pm \cos^{- 1}}\{ {\lbrack {\frac{1}{\sqrt{{\tan^{2}z_{1}} + {\tan^{2}z_{2}} + 1}} - {\cos^{2}ɛ}} \rbrack\frac{1}{\sin^{2}ɛ}} \}}} & (15)\end{matrix}$

And from Eq. 13 a has two roots α₁ and α₂

$\begin{matrix}{\alpha_{1} = {\sin^{- 1}\{ {\frac{\sqrt{\mathbb{d}{+ 1}}}{\mathbb{d}}\sin\;{ɛ\;\lbrack {{\sin\;\beta\;\tan\; z_{2}} + {( {1 - {\cos\;\beta}} )\;\cos\; ɛ\;\tan\; z_{1}}} \rbrack}} \}}} & (16) \\{d = {{\tan^{2}z_{1}} + {\tan^{2}z_{2}}}} & (17) \\{\alpha_{2} = {\pi - \alpha_{1}}} & (18)\end{matrix}$

For the embodiment shown in FIG. 4, the mathematics required to performthe transformation of the position signals to the relative positions ofthe cylinders is slightly different.

Starting with the sensor signals it is sufficient to derive themathematics using a surface simulating the rotation of the vessel.Consider z₁ and z₂ to be the angle representation of the rotation of themiddle plane in the xz-plane and yz-plane respectively. Thus the planesurface can be obtained:x tan z ₁ +y tan z ₂ +z=0  (19)

Where x, y and z are the axis in the center of the gyroscope and z isthe vertical axis aligned with gravity. Thus, the sensor is mounted ontop.

For the embodiment shown in FIG. 4, the change of height, h, on theperimeter of the cylinder due to a β rotation in the middle incline ish=h ₀ +R[sin(θ+β)−sin θ]tan ε  (20)and the rotated ellipse on the top surface is

$\begin{matrix}{{( \frac{{x\;\cos\;\beta} - {y\;\sin\;\beta}}{R} )^{2} + ( \frac{{x\;\sin\;\beta} + {y\;\cos\;\beta}}{R\;\sec\; ɛ} )^{2}} = 1} & (21)\end{matrix}$

Where h₀ is the original height of the cylinder before cutting it, R isthe radius of the cylinder, ε is the cut angle or the inclination anglefrom the vertical and θ is the polar coordinate as shown in FIG. 10B.Thus, β is the angle describing the rotation of both cylinders againsteach other to achieve the tilt.

Thus from Eq. 20, we have@θ=−90° h ₁ =h ₀ βR cos β tan ε+R tan ε  (22)@θ=+90° h ₂ =h ₀ +R cos β tan ε−R tan ε  (23)Δh=h ₂ −h ₁=2R(cos β−1)tan ε  (24)and from Eq. 21 @ x=0:

$\begin{matrix}{y_{0} = \frac{R}{\sqrt{{\sin^{2}\beta} + {\cos^{2}\beta\;\cos^{2}ɛ}}}} & (25)\end{matrix}$As shown in FIG. 10C,

$\begin{matrix}{{\sin\; z_{3}} = {\frac{\Delta\; h\;\cos\; ɛ}{2y_{0}} = {( {{\cos\;\beta} - 1} )\;\sin\; ɛ\sqrt{{\sin^{2}\beta} + {\cos^{2}\beta\;\cos^{2}ɛ}}}}} & (26)\end{matrix}$Similarly from Eq. 20, we have@θ=0 h ₃ =h ₀ +R sin β tan ε  (27)@θ=180° h ₄ =h ₀ −R sin β tan ε  (28)Δh=h ₃ −h ₄=2R sin β tan ε  (29)and from Equation 21 at y=0:

$\begin{matrix}{{x_{0} = \frac{R}{\sqrt{{\cos^{2}\beta} + {\sin^{2}\beta\;\cos^{2}ɛ}}}}{But}} & (30) \\{{\sin\; z_{4}} = {\frac{\Delta\; h\;\cos\; ɛ}{2x_{0}} = {\sin\;\beta\;\sin\; ɛ\sqrt{{\cos^{2}\beta} + {\sin^{2}\beta\;\cos^{2}ɛ}}}}} & (31)\end{matrix}$

Where z₃ is the slope in the yz-plane, z₄ is the slope in the xz-plane,(0, y₀) and (x₀, 0) are the new coordinates on the axes when the topsurface ellipse rotates by an angle β. Thus, the plane equation for thisembodiment can be described as:x tan z ₄ +y tan z ₃ +z=0  (32)

Where the coordinate axis sits on the center of the unstable surface.Rotating the axis on the top surface of the mechanism in the xy-plane anangle α corresponds to the rotation of the bottom plate of the mechanismto orient the tilt in the desired direction. Thus, the plane equationbecomes:(x cos α−y sin α)tan z ₄+(x sin α+y cos α)tan z ₃ +z=0  (33)or(tan z ₄ cos α+tan z ₃ sin α)x+(−tan z ₄ sin α+tan z ₃ cos α)y+z=0  (34)

Now, Eq. 19 and Eq. 34 must match. Thustan z ₁=tan z ₄ cos α+tan z₃ sin α  (35)andtan z ₂=−tan z ₄ sin α+tan z ₃ cos α  (36)

So, if given z₁ and z₂, a and β can be found using Eq. 26, Eq. 31, Eq.35 and Eq. 36. These two nonlinear equations with two unknowns can besolved using iterative technique or from a possible derived closed formsolution. Alternatively, instead of using iterative method a lookuptable will be derived for β.

From Eq. 35 & Eq. 36 we have the following two equations:cos α tan z ₄+sin α tan z ₃=tan z ₁  (37)−sin α tan z ₄+cos α tan z ₃=tan z ₂  (38)

Multiply Eq. 37 by sin α and multiply Eq. 38 by cos α and add yieldssin² αtan z ₃+cos² αtan z ₃=tan z ₁ sin α+tan z ₂ cos α  (39orsin α tan z ₁+cos α tan z ₂=tan z₃  (40)

Multiply Eq. 37 by cos α and multiply Eq. 38 by sin α and subtractyieldscos² αtan z ₄+sin² αtan z ₄=tan z ₁ cos α−tan z ₂ sin α  (41)orcos α tan z ₁−sin α tan z ₂=tan z ₄  (42)

Multiply Eq. 40 by tan z₂ and multiply Eq. 42 by tan z₁ and add yields

$\begin{matrix}{{{{\cos\mspace{11mu}\alpha\mspace{11mu}\tan^{2}\mspace{11mu} z_{2}} + {\cos\mspace{11mu}\alpha\mspace{11mu}\tan^{2}\mspace{11mu} z_{1}}} = {{\tan\mspace{11mu} z_{3}\mspace{11mu}\tan\mspace{11mu} z_{2}} + {\tan\mspace{11mu} z_{4}\mspace{11mu}\tan\mspace{11mu} z_{1}}}}{or}} & (43) \\{{\cos\mspace{11mu}\alpha} = \frac{{\tan\mspace{11mu} z_{3}\mspace{11mu}\tan\mspace{11mu} z_{2}} + {\tan\mspace{11mu} z_{4}\mspace{11mu}\tan\mspace{11mu} z_{1}}}{{\tan^{2}\mspace{11mu} z_{1}} + {\tan^{2}\mspace{11mu} z_{2}}}} & (44)\end{matrix}$

Multiply Eq. 40 by tan z₁ and multiply Eq. 42 by tan z₂ and subtractyields

$\begin{matrix}{{{{\sin\mspace{11mu}\alpha\mspace{11mu}\tan^{2}\mspace{11mu} z_{2}} + {\sin\mspace{11mu}\alpha\mspace{11mu}\tan^{2}\mspace{11mu} z_{1}}} = {{\tan\mspace{11mu} z_{3}\mspace{11mu}\tan\mspace{11mu} z_{1}} - {\tan\mspace{11mu} z_{4}\mspace{11mu}\tan\mspace{11mu} z_{2}}}}{or}} & (45) \\{{\sin\mspace{11mu}\alpha} = \frac{{\tan\mspace{11mu} z_{3}\mspace{11mu}\tan\mspace{11mu} z_{1}} - {\tan\mspace{11mu} z_{4}\mspace{11mu}\tan\mspace{11mu} z_{2}}}{{\tan^{2}\mspace{11mu} z_{1}} + {\tan^{2}\mspace{11mu} z_{2}}}} & (46)\end{matrix}$

Eliminate a from Eq. 44 and Eq. 46 using the identity sin²α+cos²α=1yields:(tan z ₃ tan z ₂+tan z ₄ tan z ₁)²+(tan z ₃ tan z ₁−tan z ₄ tanz²)²+(tan² z ₁+tan² z ₂)²  (47)

Squaring the terms and simplifying yields:tan² z ₃+tan² z ₄=tan² z ₁+tan² z ₂  (48)orsec² z ₃+sec² z ₄=sec² z ₁+sec² z ₂  (49)

From Eq. 26 and Eq. 31 yields

$\begin{matrix}{{\frac{1}{1 - {( {{\cos\mspace{11mu}\beta} - 1} )^{2}\sin^{2}\mspace{11mu}{ɛ( {{\sin^{2}\mspace{11mu}\beta} + {\cos^{2}\mspace{11mu}\beta\mspace{11mu}\cos^{2}\mspace{11mu} ɛ}} )}}} + \frac{1}{1 - {\sin^{2}\mspace{11mu}\beta\mspace{11mu}\sin^{2}\mspace{11mu}{ɛ( {{\cos^{2}\mspace{11mu}\beta} + {\sin^{2}\mspace{11mu}\beta\mspace{11mu}\cos^{2}\mspace{11mu} ɛ}} )}}}} = {{\sec^{2}\mspace{11mu} z_{1}} + {\sec^{2}\mspace{11mu} z_{2}}}} & (50)\end{matrix}$

To expedite the algorithm make a table of β versus the left hand of Eq.50 and pre-store the values in memories before hand. Then, for a givenz₁ and z₂ calculate the right hand side of Eq. 50 and lookup the storedtable using binary search algorithm to find the corresponding ±β. Thus,based on the previous value of β the closest β of the two is chosen perminimum energy. Finally, α is calculated from Eq. 44 or Eq. 46. Wheretan z₃=sin z₃/√{square root over (1−sin² z₃)} and tan z₄=sin z₄/√{squareroot over (1−sin² z ₄)}, sin z₃ & sin z₄are taken from Eq. 26 and Eq.31.

As an alternative to calculating the desired orientation of thecylinders, it will be appreciated that the system could be programmed torespond by moving the cylinders incrementally in response to changes inthe position sensor.

For the efficiency regarding the necessary tangential force to turn eachcylinder: If the coefficient of friction for the bearings specified bymanufacturing is 2%, thus 4% for two ball bearing, then an upper boundformula for maximum tangential force necessary to turn each cylinder canbe as follows:Top Cylinder: Force=0.04 P2+e sin(ε)P1/RBottom Cylinder: Force=0.04 P3+e sin(2ε)P1/R

Where:

-   -   P1=Weight of Helicopter only or pay load only    -   P2=Total load above the middle bearing.    -   P3=Total load above the bottom bearing    -   e=eccentricity in ft (if the helicopter is at off center- or        distance to resultant load)    -   R=radius of the slew bearing in ft    -   ε=design angle for maximum tilt=2ε

Although the described embodiments of the invention use a pair ofcylinders, it will be appreciated that the mechanism could includeadditional cylinders. For example, FIG. 6 illustrates anotheralternative embodiment of the invention. In this embodiment, a surface500 is maintained in a desired orientation by three or more cylinders502, 504, 506. Each of these cylinders is rotatable in a manner similarto that described above to adjust the angle between the cylinders and tomaintain a surface in a desired orientation.

FIG. 7 illustrates one embodiment of a computer system 552 that receivesposition signals from a position sensor 550 that detects the orientationof the surface to be adjusted or a supporting surface such as the hullof a ship. The computer 552 converts the position signals into a desiredposition of the cylinders with respect to each other and a desiredposition of the cylinders with respect to a supporting surface. Thecomputer then generates motor control signals labeled position 1,position 2 that are fed to the motors, hydraulic or pneumatic pistons orsimilar devices to move the cylinders to their desired position suchthat the orientation of the surface in question is maintained orpositioned as desired.

Although the previously described embodiments employ two cylindricalsections of substantially equal diameter to support a surface this isnot required. For example, FIG. 8 illustrates a mechanism 600 havingcylinders of unequal diameters that can be used to vary the orientationof a surface secured to the top cylinder.

Furthermore, it is not necessary to drive the cylinders at the top andbottom of the structure. It is possible to mount the motors on a bracket(for example, secured to the linkage) in order to drive the cylinders atthe slew bearing where the cylinders rotationally engage. Such aconfiguration would be required to drive the three cylinder embodimentshown in FIG. 6. Another alternative for mounting motors, specificallyelectric motors, is to mount the motors on the inside walls of thecylinders and use a conductive rotary track mounted on the linkage todeliver the electric current through such wires. Yet another alternativefor mounting the motors is to mount them completely outside thecylinders similar to the embodiment shown in FIG. 11. In this case twouniversal joints can be built inside each other, as shown in FIG. 12.The center universal joint is to have the linkage rod that controls theupper deck and the outside universal joints is to control a coincidingpipe that has gears at the top to turn the top cylinder and gears on thebottom deck to engage the motor.

In some instances, it is desirable to inhibit the movement of thecylinders with respect to a supporting surface, with respect to eachother or with respect to the surface to be maintained in a desiredorientation. As shown in FIG. 9, one or more levers 620, 622 can beadded to the mechanism to engage gears 624 of a slew bearing thatsupports a cylinder to inhibit movement of the cylinder with respect tothe slew bearing. In this manner, the support for a surface to bemaintained in a particular orientation. Upon release of the levers, thecylinders are free to move with respect to the slew bearings.

Although the described embodiments of the invention are primarilydirected towards keeping a surface level, it will be appreciated thatthe invention could also be used to keep a surface at any desired angledespite movement of a supporting structure. Similarly, the surface canbe selectively moved over a range of angles. For example, the surfacemay include a mirror and the position of the cylinders selectivelychanged so that the mirror can act as a scanning mechanism for bar-codesor the like. FIG. 11 illustrates an embodiment that can be used to movea mirror or other surface in a desired pattern for use as a scanner forexample. A mirror 700 is fixedly secured to the upper rim of an uppercylinder 702. A lower cylinder 704 is rotatably secured to a fixedsurface 706 and rotatably secured to the upper cylinder 702 at anengaging surface 708. A motor 718 drives the upper cylinder and themirror via a linkage 720 through a bearing 730. The linkage includes afirst arm 722 and a second arm 724. The second arm is connected to themirror with a joint 726 and to the first arm 722 with a universal joint728.

In this embodiment, it is not required that the joint 726 be a universaljoint (it can be a fixed joint) or that the frame of reference of themirror 700 be the same as the fixed surface 706. A motor 740 and a gear742 drive the lower cylinder 704 with respect to the fixed surface 706and the upper cylinder 702.

Although the disclosed embodiments of the invention use cylinders tosupport a surface in a desired orientation, it will be appreciated thatother column shapes could be used to support a surface such as columnsthat are triangular, square, rectangular, oval, etc., in cross-sectionprovided that the sections of the columns can be moved with respect toeach other to change the angle between them.

The embodiments shown in FIG. 3 and FIG. 4 describe a linkage with threeuniversal joints such that if there is a payload on the deck, such as ahelicopter, causing deflections of the deck the deflections will beabsorbed by the universal joints. However, if there is no payload on thedeck and only dead load or the load spans directly to the slew bearingsas for example the light scanner it has a mirror of a set weight and canbe designed to only have one universal joint at the center of FIG. 3 ortwo universal joints at the top and bottom of FIG. 4. The unuseduniversal joint/joints are replaced with a fixed connection. Thissituation can happen also in guns and artillery and so forth. Thus, thenumber of universal joints will vary per application and the requirednumber of universal joints is three or less for two cylinders orcolumns.

FIG. 13 illustrates a cross-sectional view of another embodiment of amechanism for maintaining a surface, such as a landing pad, in a desiredorientation, in accordance with the present invention. The mechanism 800includes an upper cylinder 802 and a lower cylinder 804 that arerotatably coupled along an axis 806 which is oriented at an angle withrespect to a line normal to the longitudinal axis of the cylinders 802and 804. Rotatably coupled to the top cylinder 802 is a surface 810 thatis desired to be maintained in a specific orientation. The top surface810 is secured to a fixed surface 812 that supports the lower cylinderthrough a linkage mechanism 814. A motor 820 and spur gear combination825 drive the lower cylinder with respect to the fixed surface 812.Similarly, a motor 830 and spur gear 835 drive the top cylinder withrespect to the surface 810.

Unlike the previously disclosed embodiments of the invention, therotating cylinders are coupled to each other and to the top surface 810and the fixed surface 812 with frictionless bearings. Such bearings mayinclude magnetic bearings or pneumatic frictionless bearings, etc. Forexample, the lower cylinder 804 is coupled to the fixed surface 812 witha magnetic bearing 840. The magnetic bearing 840 is preferably slopedsuch that the lower cylinder 804 remains centered on the bearing anddoes not ride off the bearing. Similarly, the upper cylinder 802 iscoupled to the top surface 810 with a magnetic bearing 850. Again, inthe embodiment shown, the bearing 850 is angled such that the topsurface 810 remains in the bearing 850 as the cylinder rotates. Inaddition, further magnetic or other frictionless bearings 860 may bepositioned at the junction of the upper cylinder 802 with the lowercylinder 804. Optional additional magnetic or frictionless bearings 870,880 and 890 can be used to counterbalance large overturning live loadmoments at the deck 810 and to keep the whole embodiment together.

With the magnetic or other frictionless bearings, the mechanism 800 canoperate with reduced power and more smoothly than if conventional ballbearing or other bearing mechanisms are used.

FIG. 14 shows yet another alternative embodiment of the presentinvention. In this embodiment of the invention, a mechanism 900 formaintaining a surface in a desired configuration includes an uppercylinder 902 and a lower cylinder 904 which are rotatably coupled alongan axis 906 that extends at an angle with respect to a lineperpendicular to the longitudinal axis of the two cylinders 902 and 904.As with the previous embodiments of the invention, the lower cylinder isrotatably coupled to a fixed surface 910 with a motor 920 and a spurgear 925. The motor and spur gear combination rotate the lower cylinder904 with respect to a fixed surface 910. An upper surface 930 is coupledto the fixed surface 910 through a linkage mechanism 940 as describedabove. However, in this embodiment of the invention, a motor 960 iscoupled to the upper surface 930 with a bracket 970. The motor 960drives a gear like a spur gear or a gear with an annular engaringsurface, which is oriented along an angled bearing 906 that joins theupper cylinder 902 to the lower cylinder 904. In this embodiment, thepinion gear coupled to the motor 960 must be able to stay in contactwith the gear regardless of the orientation of the upper and lowercylinders 902, 904. Selective orientation of the surface 930 is achievedby rotating one or both of the upper cylinder 902 and lower cylinder 904using the motors 920 and 960. As with previously disclosed embodiments,a sensor (not shown) measures the orientation of either the top surfaceor the fixed surface and a computer (not shown) drives the motors toorient the top surface in the desired position.

While the preferred embodiment of the invention has been illustrated anddescribed, it will be appreciated that various changes can be madetherein without departing from the scope of the invention. The scope ofthe invention is therefore to be determined from the following claimsand equivalents thereof.

1. A system for maintaining a surface in a desired orientation,comprising: at least two columns that are rotatably coupled alongengaging surfaces that are oriented at an angle with respect to aperpendicular cross section of the columns, said at least two columnsincluding a first column that is rotatably coupled to the surface and asecond column rotatably coupled to a supporting surface; a linkage thatjoins the surface to be maintained in a desired orientation and thesupporting surface and allows the surface to move with respect to thesupporting surface but not to rotate with respect to the supportingsurface: means for rotating the first column with respect to the secondcolumn and means for rotating the second column with respect to thesupporting surface; one or more frictionless bearings for rotatablycoupling the columns; a sensor for producing an orientation signal; anda computer for selectively driving the means for rotating the firstand/or second column to maintain the surface in the desired orientation.2. The system of claim 1, wherein the linkage has at least a first armand a second arm having a hinge at each end.
 3. The system of claim 2,wherein the hinges are universal joints.
 4. The system of claim 1,wherein the engaging surfaces are elliptical and the first and secondcolumns include a track that allows the elliptical engaging surfaces ofthe columns to rotate on each other.
 5. The system of claim 1, furthercomprising a cover that is positioned over the engaging surfaces of thefirst and second column to maintain the alignment of the first andsecond column.
 6. The system of claim 1, wherein the frictionlessbearings are magnetic levitation bearings.
 7. The system of claim 1,wherein the frictionless bearings are pneumatic.
 8. The system of claim1, wherein the surface to be maintained in a desired orientation is alanding pad.
 9. The system of claim 1, wherein the engaging surfaces ofthe first and second cylinders include Teflon bearings.
 10. The systemof claim 1, wherein the first and second columns are cylindrical.
 11. Asystem for positioning a surface in a desired orientation, comprising: afirst column rotatably coupled to a surface to be positioned in adesired orientation; a second column that is rotatably coupled to afixed surface, wherein the first and second columns are rotatablycoupled at an engaging surface and wherein the first column is coupledat an angle with respect to the surface to be positioned in a desiredorientation and the second column is coupled at an angle with respect tothe fixed surface; a linkage joining the surface and the fixed surfacethat allows the surface to move with respect to the fixed surface butnot to rotate with respect to the fixed surface; means for moving thefirst column with respect to the second column and means for moving thesecond column with respect to the fixed surface; a sensor for producinga position signals; and a computer for receiving the position andselectively operating the moving means to rotate the first and/or secondcolumns such that the surface coupled to the first column is positionedin the desired orientation.
 12. The system of claim 11, wherein thelinkage includes a first arm and a second arm, the first arm coupled tothe surface that is maintained in a desired orientation with a universaljoint and to the second arm with a universal joint, the second arm alsobeing coupled to the fixed surface with a universal joint.
 13. Thesystem of claim 11, wherein the means for moving the first column andthe means for moving the second column comprise electric motors.
 14. Thesystem of claim 11, wherein the means for moving the first column andthe means for moving the second column comprise hydraulic actuators. 15.The system of claim 11, wherein the means for moving the first columnand the means for moving the second column comprise pneumatic actuators.16. The system of claim 11, wherein the first and second columns arecylindrical.
 17. The system of claim 11 wherein the means for moving thefirst column with respect to the second column includes a motor securedto the surface and a gear that is aligned with the engaging surface ofthe first column and the second column.
 18. The system of claim 11,wherein the first and second columns are rotatably coupled withfrictionless bearings.
 19. A system for positioning a surface in adesired orientation, comprising: at least two columns that are rotatablycoupled with one or more engaging surfaces that are oriented at an anglewith respect to a perpendicular cross section of the columns, said atleast two columns including a first column that is rotatably coupled tothe surface and a second column rotatably coupled to a supportingsurface; linkage that joins the surface to the supporting surface toallow the surface to tilt with respect to the supporting surface but notto rotate with respect to the supporting surface; means for rotating thefirst column with respect to the second column and means for rotatingthe second column with respect to the supporting surface; and a computerfor selectively driving the means for rotating the first and/or secondcolumn to position the surface in the desired orientation.
 20. Thesystem of claim 19, wherein the engaging surfaces are rotatably coupledwith frictionless bearings.
 21. A system for selectively orienting asurface with respect to a fixed surface, comprising: a first cylinderrotatably coupled to the surface to be oriented; a second cylinderrotatably coupled to the fixed surface and rotatably coupled to thefirst cylinder; a linkage joining the surface to be oriented and thefixed surface such that rotation of the first cylinder with respect tothe second cylinder allows the surface to be oriented to tilt withrespect to the fixed surface but not to rotate with respect to the fixedsurface; one or more motors that move the first cylinder with respect tothe second cylinder and the second cylinder with respect to the fixedsurface; a sensor that detects the orientation of the first surface; anda computer system that controls the one or more motors to move the firstand/or second cylinder in order to selectively orient the surface.
 22. Asystem for orienting a movable surface with respect to a referencesurface, comprising: a first cylinder rotatably coupled to the movablesurface; a second cylinder rotatably coupled to the reference surfaceand rotatably coupled to the first cylinder; a linkage that joins themovable surface and the reference surface to allow the movable surfaceto tilt with respect to the reference surface but not to rotate withrespect to the reference surface; a motor coupled to the movable surfacethat engages the second cylinder to move the second cylinder withrespect to the first cylinder and a motor that moves the second cylinderwith respect to the reference surface; a sensor that produces positionsignals; and a computer that receives the position signals and activateson orient the movable surface in a desired position.
 23. The system ofclaim 22, wherein the first and second cylinders are coupled together atan angle with respect to the longitudinal axis of the cylinders.
 24. Thesystem of claim 22, wherein the first and second cylinders are coupledto the movable and reference surfaces at an angle with respect to thelongitudinal axis of the cylinders.